# A counterexample to the Hirsch conjecture

```@article{Santos2010ACT,
title={A counterexample to the Hirsch conjecture},
author={Francisco Santos},
journal={ArXiv},
year={2010},
volume={abs/1006.2814}
}```
• F. Santos
• Published 2010
• Computer Science, Mathematics
• ArXiv
The Hirsch Conjecture (1957) stated that the graph of a d-dimensional polytope with n facets cannot have (combinatorial) diameter greater than n d. That is, any two vertices of the polytope can be connected by a path of at most n d edges. This paper presents the rst counterexample to the conjecture. Our polytope has dimension 43 and 86 facets. It is obtained from a 5-dimensional polytope with 48 facets that violates a certain generalization of the d-step conjecture of Klee and Walkup.
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